InterviewSolution
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InterviewSolution
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The value of `sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)]`is equal to`sin^(-1)x+sin^(-1)sqrt(x)``sin^(-1)x-sin^(-1)sqrt(x)``sin^(-1)sqrt(x)-sin^(-1)x`none of theseA. `sin^(-1) x + sin^(-1) sqrtx`B. `sin^(-1) x - sin^(-1) sqrtx`C. `sin^(-1) sqrtx - sin^(-1) x`D. none of these |
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Answer» Correct Answer - B Let `x = sin theta and sqrtx = sin phi, " where " x in [0, 1]` `rArr theta, phi in [0, pi//2]` `rArr theta - phi in [(-pi)/(2), (pi)/(2)]` Now, `sin^(-1) (x sqrt(1 -x) - sqrtx sqrt(1 - x^(2)))` `= sin^(-1) (sin theta sqrt(1 - sin^(2) phi) - sin phi sqrt(1 - sin^(2) theta))` `= sin^(-1) (sin theta cos phi - sin phi cos theta)` `= sin^(-1) sin (theta - phi) = theta - phi` `= sin^(-1) (x) - sin^(-1) (sqrtx)` |
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